The course is focused on the study of the industrial robotic manipulators. More precisely, the kinematics and the dynamics of robotic manipulators are deeply investigated. The trajectory planning problem is analyzed and several planning schemes are proposed.
At the course conclusion, the student should be able to:
- Use the mathematical tools adopted for the description of objects in 3D environments;
- Solve direct and inverse kinematics problems;
- Solve direct and inverse dynamics problems;
- Evaluate velocities and accelerations of robotic arms;
- Plan simple trajectories.
Course contents summary
- Introduction to industrial robotics (1 hour)
Basic concepts on the mechanics and control of robotic manipulators.
- Reference systems and transformations (9 hours)
Description of joints positions and orientations. The rotational matrix. Translational and rotational operators. Minimum-order orientation notations: Fixed angles, Euler angles, angle-axis representation, Euler parameters. Computational considerations.
- Direct kinematics (4 hours)
Classification and description of robotic joints. Description of the links position and orientation: the modified Denavit-Hartenberg notation. The homogeneous transformation matrix. Joint space, operational space and manipulator workspace.
- Inverse kinematics (6 hours)
The solvability of the inverse kinematics problem. Geometric and algebraic solutions.
- Differential kinematics and static forces (12 hours)
Rigid bodies linear and angular velocities. The Jacobian matrix and its properties. Manipulator static forces: the forward recursive algorithm and the Jacobian approach.
- Dynamics (4 hours)
The inertia tensor matrix. Bodies center of mass. Inverse dynamics: the Newton-Euler backward recursive formulation. Direct dynamics: solution by means of simulation programs.
- Trajectory planning (12 hours)
Joint space trajectories. Point-to-point and multipoint trajectory generation using cubic polynomials. Point-to-point and multipoint trajectory generation using linear-quadratic functions. Operational space trajectories. Kinematics singularities.
C. Guarino Lo Bianco, `` Analisi e controllo dei manipolatori industriali“, seconda edizione, Pitagora editrice, Bologna,Italia 2011.
L.Sciavicco e B.Siciliano, ``Robotica industriale: modellistica, pianificazione e controllo'', terza edizione, McGraw-Hill Italia, 2008.
J.Craig, ``Introduction to Robotics'', terza edizione, Pearson, 2005.
Several exercitations are scheduled in the Didactical Lab in order to simulate the control of an industrial manipulator.
Assessment methods and criteria
The final test is divided into two written parts:
in the first one (Parte A), which lasts 1h:30m, the student must solve the direct and the inverse kinematics of a manipulator (maximum score 32/30);
in the second one (Parte B), which lasts 1h:30m, he must answer to questions concerning the course theoretical topics (maximum score 32/30).
The exam is passed if a score higher than 18/30 is gained in both the two parts.
"Parte A" can be passed by means of two intermediate test sessions carried out during the lessons period.
The final score is obtained as a mean between the scores of the two parts. A maximum of two further points can be gained for the Lab activity executed during the lesson period.
The "Laude" grade is assigned if the final score is higher than 30/30.